Question

A capacitor is made from two hollow, coaxial, iron cylinders, one inside the other. The inner cylinder is negatively charged and the outer is positively charged; the magnitude of the charge on each is 12.0 pC . The inner cylinder has a radius of 0.500 mm , the outer one has a radius of 7.60 mm , and the length of each cylinder is 24.0 cm .

Part A

What is the capacitance?

Use 8.854×10⁻¹² F/m for the permittivity of free space.

C=___ F

Part B

What applied potential difference is necessary to produce these charges on the cylinders?

V=___ V

Answer 1

(A)

Capacitance of the coaxial capacitor is,

C = 2πεo L / ln( b / a)

              = 2π (8.854×10⁻¹² ) (0.24 m)/ ln(7.6 / 0.5 )

                = 4.90*10^-12 F

                =4.90 pF

(B)

The applied potential difference is necessary to produce these charges on the cylinders is,

                    V = Q / C

                        = (12.0 pC)/(4.90 pF)

                       =2.45 V